In my joke about set theory in Latin:
Hodie in universitate (ego studeo scientiam computorum) docebamur de theoria unionum. Professor nobis explicabat, cur numerus cardinalis unionis unionum non semper sit summa (additio) cardinalum numerorum unionum: "Si hoc veritas esset, canis debet octo crura habere. Canis enim habet duo crura antica, duo crura posteriora, duo crura laeva, et duo crura dextera. Summa (additio) numerorum cardinalium earum unionum octo (quater bini) est, sed numerus cardinalis unionis earum unionum, sane, quattuor est.".
I was using the same word, "unio", for both the union and the set. That caused some people to not be able to understand my joke. So, how could I have done better? Which word should I use for "set" and which for "union"?
By "set" I mean a group of things with some common property. And by "union" I mean the operation on two sets that gives another set that contains all the elements that were contained in the first set or the second set or both.